Cycles Glass BSDF on a Diamond viewport problem
From my experience in Blender, a more complex diamond mesh gives the light more directions to scatter, which will increase the number of refraction effects you can detect on the surface.
In jeweler's terms, the cut of the diamond influences the clarity, sparkle, and brilliance.  Sometimes these are at odds with each other.

Also, increasing the number of Glossy and Total bounces under Light Paths will get rid of these dark areas.